1		Overview and Definitions

Definitions and Overview 1

List of Symbols

The following symbols are used throughout these notes. However, no universal defining standard for their use exists. Other books on the subject may use some of these symbols with different definitions. Every effort has been made to employ symbols that are widely accepted and that conform to the Learning Objectives.

a	speed of sound
AC	aerodynamic centre
AR	aspect ratio
b	span
C	Centigrade
c	chord length
CD	drag coefficient
CG	centre of gravity
CP	centre of pressure
CL	lift coefficient
CM	pitching moment coefficient
D	drag
Di	induced drag
F	force
g	acceleration due to gravity, also used for load factor

KKelvin

Llift

L/D	lift to drag ratio
M	Mach number

mmass

nload factor

p pressure

Q or q dynamic pressure

Sarea; wing area

Ttemperature

t/c	thickness-chord ratio
V	free stream speed (TAS)
VS	stall speed
W	weight

Greek Symbols

α (alpha) angle of attack

β(beta) sideslip angle

γ(gamma) angle of climb or descent (delta) increment in

μ (mu) Mach angle

ρ(rho) density

σ (sigma) relative density

φ(phi) angle of bank

14

Overview and Definitions		1

Others

proportional to

•

= is approximately equal to

•

Note: The Greek symbol γ (gamma) has been used in these notes to denote angle of climb and descent. The Learning Objectives use θ (theta). Evidence exists that a question in the exam uses γ (gamma) for angle of climb and descent. The notes have been amended to use γ, but consider either γ or θ to indicate angle of climb and descent.

Overview and Definitions 1

15

1 Questions

Questions 1

Self-assessment Questions

Aircraft (1)

Mass: 2000 kilograms (kg)

Engine thrust: 4000 newtons (N)

V1 speed: 65 knots (kt)

Take-off run to reach V1: 750 metres (m)

Time taken to reach V1: 30 seconds (s)

Aircraft (2)

Mass: 2000 kilograms (kg)

Engine thrust: 8000 newtons (N)

V1 speed: 130 knots (kt)

Take-off run to reach V1: 1500 metres (m)

Time taken to reach V1: 40 seconds (s)

where 1 nautical mile = 6080 ft and 1 metre = 3.28 ft

At V1 both aircraft experience an engine failure and take-off is abandoned.

a.How much work was done to aircraft (1) getting to V1?

b.How much power was used to get aircraft (1) to V1?

c.How much work was done to aircraft (2) getting to V1?

d.How much power was used to get aircraft (2) to V1?

e.How much momentum does aircraft (1) possess at V1?

f.How much momentum does aircraft (2) possess at V1?

g.How many times greater is the momentum of aircraft (2)?

h.How much kinetic energy does aircraft (1) possess at V1?

i.How much kinetic energy does aircraft (2) possess at V1?

j.How many times greater is the kinetic energy of aircraft (2)?

k.State the mass and velocity relationship of both aircraft and compare to their momentum and kinetic energy.

l.Which has the greater effect on kinetic energy, mass or velocity?

m.What must be done with the kinetic energy so the aircraft can be brought to a stop?

16

Questions 1

1.An aircraft’s mass is a result of:

a.its weight.

b.how big it is.

c.how much matter it contains.

d.its volume.

2.The unit of mass is the:

a.joule.

b.watt.

c.newton.

d.kilogram.

3.The definition of a force is:

a.that which causes a reaction to take place.

b.thrust and drag only.

c.a push or a pull.

d.the result of an applied input.

4.The unit of force is the:

a.mass-kilogram.

b.newton-metre.

c.joule.

d.newton.

5.The unit of weight is the:

a.kilogram.

b.newton.

c.watt.

d.kilowatt.

6.Weight is the result of:

a.the force on mass due to gravity.

b.the action of a falling mass.

c.how much matter the object contains.

d.the rate of mass per unit area.

7.About which point does an aircraft rotate?

a.The wings.

b.The main undercarriage.

c.The centre of gravity.

d.The rudder.

8.If a force is applied to a mass and the mass does not move:

a.work is done even though there is no movement of the mass.

b.work is done only if the mass moves a long way.

c.power is exerted, but no work is done.

d.no work is done.

Questions 1

17

		1		Questions
				9.	The unit of work is called the:
	1
	Questions				a.	pascal.
					b.	joule.
					c.	watt.
					d.	kilogram.
				10.	The unit of power is called the:
					a.	joule.
					b.	newton-metre.
					c.	watt.
					d.	metre per second.
				11.	If a force of 20 newtons moves a mass 5 metres:
					1 - the work done is 100 Nm
					2 - the work done is 100 joules
					3 - the work done is 4 joules
					4 - the work done is 0.25 joules
					The correct statements are:
					a.	1 only.
					b.	1 and 3.
					c.	1 and 2.
					d.	2 only.
				12.	If a force of 50 newtons is applied to a 10 kg mass and the mass moves 10 metres
					and a force of 50 newtons is applied to a 100 kg mass which moves 10 metres:
					a.	the work done is the same in both cases.
					b.	less work is done to the 10 kg mass.
					c.	more work is done to the 10 kg mass.
					d.	more work is done to the 100 kg mass.
				13.	The definition of power is:
					a.	the rate of force applied.
					b.	the rate of movement per second.
					c.	the rate of doing work.
					d.	the rate of applied force.
				14.	If a force of 500 newtons moves a mass 1000 metres in 2 mins, the power used is:
					a.	4167 watts.
					b.	250 kilowatts.
					c.	1 megawatt.
					d.	4 watts.
				15.	Kinetic energy is:
					a.	the energy a mass possesses due to its position in space.
					b.	the energy a mass possesses when a force has been applied.
					c.	the energy a mass possesses due to the force of gravity.
					d.	the energy a mass possesses because of its motion.

18

				Questions		1
	16.	The unit of kinetic energy is the:
					1
		a.		joule.		Questions
		b.		metre per second.
		c.		watt.
		d.		newton-metre per second.
	17.	When considering kinetic energy:
		1	- a moving mass can apply a force by being brought to rest.
		2	- kinetic energy is the energy possessed by a body because of its motion.
		3	- if a body’s kinetic energy is increased, a force must have been applied.
		4	- kinetic energy = ½ m V2 joules.
		The combination of correct statements is:
		a.		1 and 2.
		b.		1, 2, 3 and 4.
		c.		4 only.
		d.		2 and 4.
	18.	The property of inertia is said to be:
		a.		the energy possessed by a body because of its motion.
		b.		the opposition which a body offers to a change in motion.
		c.		that every action has an equal and opposite reaction.
		d.		the quantity of motion possessed by a body.
	19.	Considering Newton’s first law of motion:
		1	- a body is said to have energy if it has the ability to do work.
		2	- the amount of energy a body possesses is measured by the amount of work it
				can do.
		3	- a body will tend to remain at rest, or in uniform motion in a straight line, unless
				acted upon by an external force.
		4	- to move a stationary object or to make a moving object change its direction, a
				force must be applied.
		The combination with the correct statements is:
		a.		3 and 4.
		b.		3 only.
		c.		1 and 2.
		d.		1, 2, 3 and 4.

19

		1		Questions
				20.	Considering Newton’s second law of motion:
	1
	Questions				1 - every action has an equal and opposite reaction.
					2 - if the same force is applied, the larger the mass the slower the acceleration.
					3 - if two forces are applied to the same mass, the bigger the force the greater the
						acceleration.
					4 - the acceleration of a body from a state of rest, or uniform motion in a straight
						line, is proportional to the applied force and inversely proportional to the mass.
					The combination of true statements is:
					a.	1 only.
					b.	1, 2, 3 and 4.
					c.	2, 3, and 4.
					d.	3 and 4.
				21.	Newton’s third law of motion states:
					a.	the energy possessed by a mass is inversely proportional to its velocity.
					b.	every force has an equal and opposite inertia.
					c.	for every force there is an action.
					d.	every action has an equal and opposite reaction.
				22.	The definition of velocity is the:
					a.	rate of change of acceleration.
					b.	rate of change of displacement.
					c.	the quantity of motion possessed by a body.
					d.	the acceleration of a body in direct proportion to its mass.
				23.	When considering acceleration:
					1 - acceleration is the rate of change of velocity.
					2 - the units of acceleration are metres per second.
					3 - the units of acceleration are kilogram-metres per second.
					4 - the units of acceleration are seconds per metre per metre.
					The combination of correct statements is:
					a.	4 only.
					b.	1 and 4.
					c.	1 only.
					d.	1 and 2.
				24.	The definition of momentum is:
					a.	the quantity of mass possessed by a body.
					b.	the quantity of inertia possessed by a body.
					c.	the quantity of motion possessed by a body.
					d.	the opposition which a body offers to a change in velocity.

20

				Questions		1
	25.	A force of 24 newtons moves a 10 kg mass 60 metres in 1 minute. The power used
					1
		is:
						Questions
		1	- 24 watts.
		2	- 240 watts.
		3	- force times distance moved in one second.
		4	- force times the distance the mass is moved in one second.
		Which of the preceding statements are correct:
		a.		1 and 3.
		b.		1, 3 and 4.
		c.		2 and 4.
		d.		4 only.
	26.	When considering momentum:
		1	- momentum is the quantity of motion possessed by a body.
		2	- momentum is the tendency of a body to continue in motion after being placed
				in motion.
		3	- a mass of 2000 kg moving at 55 m/s has 110 000 kg-m/s of momentum.
		4	- a large mass moving at 50 m/s will have less momentum than a small mass
				moving at 50 m/s.
		The correct combination of statements is:
		a.		1 and 3.
		b.		1, 2, 3 and 4.
		c.		1, 2 and 3.
		d.		2, 3 and 4.

21